I have OS backup .dmg installation file. The problem is I have Windows 7 on my MacBook Air, and I do not have access to OS X to use Disk Utility to burn/restore the OS X image.
Is it possible to burn/restore .dmg file on usb stick from Windows?
You dont need accessing it from windows.
Boot the computer holding the [option] key and choose the OSX recovery. Inside it there you'll have a very basic osx with its own Disk Utility to restore your DMG image to another USB.
Several programs that support opening DMG files:
7-Zip will let you unzip the files. You can rebuild and burn an ISO image from there. http://sourceforge.net/projects/sevenzip/
A search around the web brought up TransMac as being able to directly burn a DMG to disk: http://www.asy.com/sharetm.htm
Same goes for UltraISO: http://www.ezbsystems.com/ultraiso/download.htm
... but I've not tried them.